Hey Kristy and Jessie!
Unfortunately no, currently there is no way to control the order in which facets options appear. We hear you, though, and we’re considering ways to make facet order configurable.
The name (i.e. “Answers Specialty”) of the facet filter pulls directly from the Display Name of the field itself, so you’d have to change that in your account settings. There is no way to override it on the front-end.
Hope that helps!